{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## —————————————————————————————————————————————————  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=5>姓名：冉成林   学号：20201120466   专业：电子科学与技术</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=5>邮箱：2033947824@qq.com</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=6>Project #4</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=5>利用贝塞尔曲线作图</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=center> <img src=\"https://s1.328888.xyz/2022/05/14/qDLx2.webp\" width=\"600\"></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><font size=4>日期：2022.5.14</font></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## ——————————————————————————————————————————————————"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction（项目介绍）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "贝塞尔曲线（Bezier curves）是插值（Interpolation）的一个非常重要的应用，可以用有限的坐标点表示多样的图形，大大增强了计算机的图形显示效果。\n",
    "\n",
    "本项目我们将利用贝塞尔曲线实现对简单的图形和字母的表示，最终的项目效果如下图所示。\n",
    "\n",
    "\n",
    "<img src = \"https://s1.328888.xyz/2022/05/14/qDyF3.png\" width=500>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Original image（给出原始图形）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--- 替换下面的图片链接为你的图片链接，可以是本地的也可以网络上的图片 --->\n",
    "\n",
    "<img src = \"https://s1.328888.xyz/2022/05/14/qDu0Q.png\" width = 400>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Data extracted from image（提取原始数据）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "PositionOfImage = [\n",
    "    [2.41, 13.83, 1.9, 13.47, 1.24, 12.3, 0.9, 11.9,0.4,12.27],\n",
    "    [3.7, 13.8, 2.04, 12.53, 1.73, 11.78, 1.38, 11.38,0.47,10.93],\n",
    "    [4.6, 13.6, 3.8, 11.8, 3.87, 11.22, 4.18,9.8],\n",
    "    [5.07, 12.18, 4.38, 11, 4.18, 10.5, 4.16,9.8],\n",
    "    [5.02, 12.45, 5.18, 11.2, 5.40, 10.45, 5.63,10.17],\n",
    "    [5.47,12.08,5.63,10.17],\n",
    "    [0.4, 12.17, 1.04, 11.6, 1.4, 11.6, 1.54,11.68],\n",
    "    [0.47,10.93, 1.74, 10.96, 2.46, 11.2, 2.78,11.42],\n",
    "    [3.07, 12.77, 2.4, 10.8, 3.2, 8.18, 3.64, 7.86,4.02,7.52],\n",
    "    [1.4,11,0.98,10.1,0.8,9.28],\n",
    "    [0.8,9.28,1.18,9.58,1.68,9.83],\n",
    "    [1.68,9.83,1.51,9.26,1.18,8.82,0.67,8.59],\n",
    "    [0.67,8.59,1.78,8.58,2.41,8.82],\n",
    "    [2.78,9.88,2.31,8.92,2.2,8.33,2.22,7.61],\n",
    "    [3.46,10.65,3.18,9.8,3.39,10.04,3.47,8.36,4.02,7.53],\n",
    "    [3.9,10.98,3.32,9.63,3.3,9.2],\n",
    "    [5.6,10.72,5.84,9.84,6.36,9.18],\n",
    "    [4.25,10.52,4.95,10.54,5.66,10.16,5.78,9.94],\n",
    "    [3.58,10.08,3.73,10.27,4.57,10.46,5.27,10.23,5.68,9.8],\n",
    "    [4.3,9.01,4.52,8.87,5,8.88,5.16,8.9,5.7,9.34,5.43,9.87],\n",
    "    [3.6,10,3.73,9.48,4.18,9.26,4.3,9.01],\n",
    "    [3.64,7.84,4.04,6.48,4.85,6.05,5.48,5.64,6.24,5.24],\n",
    "    [6.24,5.24,6.75,5.38,7.78,5.98,8.46,6.44,8.86,7.34],\n",
    "    [2.2,7.6,2.33,8.04,2.5,8.24],\n",
    "    [2.5,8.24,2.51,7.35,2.78,6.58,3,6.5],\n",
    "    [3,6.5,2.97,7,2.98,7.84],\n",
    "    [2.98,7.84,3.01,7.21,3.2,7.02],\n",
    "    [3.2,7.02,3.18,8.18,3.22,8.43],\n",
    "    [3.2,7.95,3.38,7.63,3.48,7.54,3.64,7.45,3.8,7.41],\n",
    "    [2.97,6.4,3.18,6.42,3.3,6.84],\n",
    "    [3.3,6.84,3.32,6.26,3.15,5.75],\n",
    "    [3.15,5.75,3.57,6,3.77,6.5],\n",
    "    [3.77,6.5,3.65,6.02,3.64,5.68],\n",
    "    [3.64,5.68,3.78,6,3.93,6.2],\n",
    "    [3.93,6.2,4.02,5.72,3.91,5.2],\n",
    "    [3.91,5.2,4.22,5.48,4.25,5.73],\n",
    "    [4.3,5.01,4.35,5.76,4.13,6.64],\n",
    "    [4.55,5.92,4.62,5.62],\n",
    "    [4.64,5.52,4.72,5.21,4.92,4.85],\n",
    "    [4.12,5.03,4.83,4.8,6.18,4.66],\n",
    "    [4.12,5.03,4.1,4.75],\n",
    "    [3.82,4.78,6.08,4.42,6.2,4.39],\n",
    "    [6.2,4.39,6.22,3.98,6.2,2.47],\n",
    "    [3.82,4.78,3.63,3.37,3.64,2.97,3.65,2.98],\n",
    "    [3.65,2.98,6.21,2.48],\n",
    "    [6.21,2.48,6.3,2.42],\n",
    "    [6.21,2.48,1.4,1.78],\n",
    "    [1.4,1.78,1.34,1.77,1.22,1.68,1.18,1.15],\n",
    "    [0.07,2.78,1.15,3],\n",
    "    [0.07,2.78,-0.83,2.65,-1.02,2.62,-1.05,2.55,-1.16,2.35,-1.15,2.26,-1.08,1.81],\n",
    "    [0.08,2.32,-0.41,2.25,-0.96,2.08,-1.08,1.81],\n",
    "    [-1.08,1.81,-1.18,1.32,-1.07,1],\n",
    "    [-1.15,2.35,-1.54,1.97,-1.78,1.38,-1.87,1],\n",
    "    [0.6,2.88,-1.4,4.63,-3.7,6.22,-4.8,6.74,-6.8,8.5],\n",
    "    [-3.8,2.57,-4.3,3.21,-5.3,4.18,-5.96,4.28,-6.75,4.64,-7.23,5.35],\n",
    "    [-3.8,2.57,-4.5,2.8,-5.98,2.97,-5.64,3.02,-6.2,3.18,-6.6,3.43],\n",
    "    [1.28,3.14,1.04,2.97,1.01,2.8,1.13,2.52],\n",
    "    [1.13,2.52,0.08,2.32],\n",
    "    [1.13,2.52,1.18,2.5,1.82,2.63,1.84,2.68],\n",
    "    [1.84,2.68,1.73,2.92,1.9,3.19],\n",
    "    [1.9,3.19,1.91,3.26],\n",
    "    [1.91,3.26,1.28,3.13],\n",
    "    [1.84,2.68,2.95,2.96,3.03,3.07],\n",
    "    [3.03,3.07,3.4,3.59],\n",
    "    [1.91,3.26,1.90,3.38,2.07,3.58,2.82,3.63,2.9,3.5],\n",
    "    [2.9,3.5,3.72,3.63],\n",
    "    [2.9,3.5,2.88,3.38,2.43,3.08,1.98,3.03,1.91,3.2],\n",
    "    [4.84,1.76,5.33,1.92,6.4,2.14],\n",
    "    [6.17,4.67,6.19,4.42,6.28,4.41],\n",
    "    [5.99,8.01,6.11,7.91],\n",
    "    [6.56,7.9,6.68,7.98],\n",
    "    [5.73,6.99,6.7,6.88],\n",
    "    [6.7,6.88,6.35,7.1,6.03,7.12,5.95,6.96],\n",
    "    [4.49,9.82,4.31,9.5,4.6,9.1,5.11,9.19,5.25,9.4,5.28,9.84,4.75,10.09,4.49,9.82],\n",
    "    [4.8,9.71,4.92,9.73,4.98,9.59,4.91,9.47,4.81,9.45,4.71,9.47,4.68,9.6,4.71,9.70,4.8,9.71],\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将三个字母对应的数据填入下面的python列表\n",
    "PositionOfLetter_1 =[\n",
    "    [-5.3,9,-5.3,11],\n",
    "    [-5,9.9,-5,9],\n",
    "    [-5,10.15,-5,10.8],\n",
    "    [-5,9,-5.3,9],\n",
    "    [-5.3,11,-4.4,11],\n",
    "    [-5,10.8,-4.4,10.8],\n",
    "    [-5,10.15,-4.4,10.15],\n",
    "    [-5,9.9,-4.6,9.9],\n",
    "    [-4.4,10.8,-4.16,10.81,-3.98,10.61,-3.97,10.42,-4.05,10.16,-4.4,10.15],\n",
    "    [-4.6,9.9,-4.33,9.9,-3.86,9],\n",
    "    [-3.86,9,-3.52,9],\n",
    "    [-3.52,9,-3.76,9.36,-3.97,9.79,-4.28,9.9],\n",
    "    [-4.28,9.9,-4.02,9.96,-3.7,10.18,-3.67,10.5,-3.71,10.76,-4,11,-4.4,11]\n",
    "]\n",
    "\n",
    "PositionOfLetter_2 =[\n",
    "    [-1.6,10.44,-1.8,11.1,-2.3,11.4,-3.4,11.2,-3.58,10,-3.33,8.8,-2.6,8.79,-1.8,8.8,-1.6,9.6],\n",
    "    [-1.6,10.44,-1.88,10.4],\n",
    "    [-1.6,9.6,-1.88,9.7],\n",
    "    [-1.88,10.4,-1.98,10.8,-2.6,10.88,-3.08,10.55,-3.08,9.61,-2.8,9.2,-2.22,9.2,-1.88,9.7]\n",
    "]\n",
    "\n",
    "PositionOfLetter_3 =[\n",
    "    [-1.26,9,-1.26,11],\n",
    "    [-1,11,-1,9.25],\n",
    "    [-1,11,-1.26,11],\n",
    "    [-1.26,9,0,9],\n",
    "    [0,9.25,0,9],\n",
    "    [-1,9.25,0,9.25]\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Python function for Bezier curves（贝塞尔曲线的python函数）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 计算某一个t对应的贝塞尔曲线的坐标"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 三阶贝塞尔函数的python表示\n",
    "def bezier3(t, P):\n",
    "    # 从P中提取四个坐标的数据\n",
    "    P0 = P[0]\n",
    "    P1 = P[1]\n",
    "    P2 = P[2]\n",
    "    P3 = P[3]\n",
    "    \n",
    "    # 逐步构造贝塞尔曲线的坐标\n",
    "    A = (1 - t) * P0 + t * P1\n",
    "    B = (1 - t) * P1 + t * P2\n",
    "    C = (1 - t) * P2 + t * P3\n",
    "    \n",
    "    D = (1 - t) * A + t * B\n",
    "    E = (1 - t) * B + t * C\n",
    "    \n",
    "    return (1 - t) * D + t * E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 三阶贝塞尔函数的python表示\n",
    "# 上面的python函数，可以简化成一个比较简单的形式\n",
    "# 即把对应的A、B、C、D、E替换到最后的return后面的公式\n",
    "def bezier3v2(t, P):\n",
    "    # 从P中提取四个坐标的数据\n",
    "    # P0 = P[0]\n",
    "    # P1 = P[1]\n",
    "    # P2 = P[2]\n",
    "    # P3 = P[3]\n",
    "    \n",
    "    # 逐步构造贝塞尔曲线的坐标\n",
    "    # A = (1 - t) * P0 + t * P1\n",
    "    # B = (1 - t) * P1 + t * P2\n",
    "    # C = (1 - t) * P2 + t * P3\n",
    "    \n",
    "    # D = (1 - t) * A + t * B = (1 - t) * (1 - t) * P0 + (1 - t) * t * P1 + t * (1 - t) * P1 + t * t * P2\n",
    "    # E = (1 - t) * B + t * C = (1 - t) * (1 - t) * P1 + (1 - t) * t * P2 + t * (1 - t) * P2 + t * t * P3\n",
    "    \n",
    "    # (1 - t) * D + t * E = (1 - t)^3 * P0 + 3 * (1 - t)^2 * t * P1 + 3 * (1 - t) * t^2 * P2 + t^3 * P3\n",
    "    \n",
    "    return (1 - t)**3 * P[0] + 3 * (1 - t)**2 * t * P[1] + 3 * (1 - t) * t**2 * P[2] + t**3 * P[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 验证上面的函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = [0, 0, 1, 1, 2, 1, 3, 0]\n",
    "P = np.array(P).reshape((4,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6 , 0.48])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bezier3(0.2, P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6 , 0.48])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bezier3v2(0.2, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出，两个函数的返回结果一致"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 任意阶贝塞尔曲线计算函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以用两种办法实现任意阶贝塞尔曲线的计算函数，一种是采用两个循环，另一种是采用函数递归。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bezierN_v1(t, P):\n",
    "    n = P.shape[0]\n",
    "    for i in range(n - 1):\n",
    "        Ptemp = np.zeros((P.shape[0] - 1, 2))\n",
    "        for j in range(P.shape[0] - 1):\n",
    "            Ptemp[j] = (1 - t) * P[j] + t * P[j + 1]\n",
    "        P = Ptemp\n",
    "    return P[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6 , 0.48])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bezierN_v1(0.2, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可见结果与三阶的计算一致"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bezierN_v2(t, P):\n",
    "    if P.shape[0] == 2:\n",
    "        return (1 - t) * P[0] + t * P[1]\n",
    "    return bezierN_v2(t, (1 - t) * P[:-1] + t * P[1:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6 , 0.48])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bezierN_v2(0.2, P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "递归代码少，计算结果也一致，体现了现代编程思想。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Python function for route calculation（完整的贝塞尔曲线路径计算） "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 定义路径计算函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def route(P, bezier = bezier3v2):\n",
    "    # 上面传入了一个bezier参数，这里是计划采用的bezier计算函数的名称\n",
    "    # 可以是我们上面写的任意一个贝塞尔python函数，可以根据各自的情况自由选择\n",
    "    # 这里我们默认采用bezier3v2\n",
    "    \n",
    "    # 定义一个tList来承载所有的t\n",
    "    numberOfPoints = 101\n",
    "    tList = np.linspace(0, 1, 101)\n",
    "    \n",
    "    # 初始化一个数组来承载所有的路径坐标\n",
    "    arrP = np.zeros((numberOfPoints, 2))\n",
    "    \n",
    "    # 开始计算\n",
    "    index = 0\n",
    "    for t in tList:\n",
    "        arrP[index, :] = bezier(t, P)\n",
    "        index += 1\n",
    "        \n",
    "    return arrP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 验证路径计算函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "arrP = route(P, bezier = bezier3v2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x229195c3160>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(arrP[:, 0], arrP[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Draw image and letters（画图以及画字符）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def route(P, bezier = bezierN_v1):\n",
    "    numberOfPoints = 101\n",
    "    tList = np.linspace(0, 1, 101)\n",
    "    arrP = np.zeros((numberOfPoints, 2))\n",
    "    index = 0\n",
    "    for t in tList:\n",
    "        arrP[index, :] = bezier(t, P)\n",
    "        index += 1\n",
    "        \n",
    "    return arrP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 14.0)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 10))\n",
    "for P in PositionOfImage:\n",
    "    P=np.array(P)\n",
    "    a=P.size\n",
    "    P = np.array(P).reshape((a//2, 2))\n",
    "    arrP = route(P)\n",
    "    plt.plot(arrP[:, 0], arrP[:, 1],'k',linewidth=3)\n",
    "\n",
    "# 画出第1个字母的贝塞尔曲线\n",
    "for P in PositionOfLetter_1:\n",
    "    P=np.array(P)\n",
    "    a=P.size\n",
    "    P = np.array(P).reshape((a//2, 2))\n",
    "    arrP = route(P)\n",
    "    plt.plot(arrP[:, 0], arrP[:, 1], 's-')\n",
    "    \n",
    "# 画出第2个字母的贝塞尔曲线\n",
    "for P in PositionOfLetter_2:\n",
    "    P=np.array(P)\n",
    "    a=P.size\n",
    "    P = np.array(P).reshape((a//2, 2))\n",
    "    arrP = route(P)\n",
    "    plt.plot(arrP[:, 0], arrP[:, 1], 's-')\n",
    "\n",
    "# 画出第3个字母的贝塞尔曲线\n",
    "for P in PositionOfLetter_3:\n",
    "    P=np.array(P)\n",
    "    a=P.size\n",
    "    P = np.array(P).reshape((a//2, 2))\n",
    "    arrP = route(P)\n",
    "    plt.plot(arrP[:, 0], arrP[:, 1], 's-')\n",
    "    \n",
    "plt.xlim(-6.5, 6.5)\n",
    "plt.ylim(1, 14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Share my experience"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.由于动漫人物的图形线条比较多，且对线条的精确性要求比较高。为了节约时间，放弃了之前先求控制点的方法，采取了用AutoCAD作为辅助软件的画法。接下来我就讲讲在用AutoCAD的时候发现的一些规律。\n",
    "### 2.控制点越多，对线的拟合会越精确，但有可能会遇到比较麻烦的控制点调整情况。\n",
    "### 3.前两个控制点和最后两个控制点的分别连线，对应起点和终点的切线。\n",
    "### 4.曲线只经过第一控制点和最后一控制点（直线除外）\n",
    "### 5.作图时更多用的分段贝塞尔曲线，结合3来看，只需要将分段曲线连接处的控制点以连接点做点对称就可以达到相切平滑的目的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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